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Mathematics

Assertion (A) : If the class-mark of a class is 9.5 and the class size is 6, then the class interval is 6 - 12.

Reason (R) : Class mark = upper limit + lower limit2\dfrac{\text{upper limit + lower limit}}{2}

  1. A is true, R is the false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false.

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Answer

As we know,

Class mark = upper limit + lower limit2\dfrac{\text{upper limit + lower limit}}{2} …(1)

∴ Reason (R) is true.

Given,

Class mark = 9.5

Class size = 6

Let upper limit be U and lower limit be L.

Susbtituting values in eq.(1), we get:

Class mark = Lower limit + Upper limit2\dfrac{\text{Lower limit + Upper limit}}{2}

⇒9.5=L + U2⇒L + U=9.5×2⇒L + U=19….(2)\Rightarrow 9.5 = \dfrac{\text{L + U}}{2} \\[1em] \Rightarrow \text{L + U} = 9.5 \times 2 \\[1em] \Rightarrow \text{L + U} = 19 ….(2)

Class size = Upper limit - Lower limit = U - L

⇒ 6 = U - L ….(3)

Adding eq.(2) and (3), we have:

⇒ 19 + 6 = 2U

⇒ 2U = 25

⇒ U = 252\dfrac{25}{2}

⇒ U = 12.5

Substituting value of U in eq.(2), we have:

⇒ L + U = 19

⇒ L + 12.5 = 19

⇒ L = 19 - 12.5

⇒ L = 6.5

∴ Class interval is 6.5 - 12.5

∴ Assertion (A) is false.

Hence option 2 is the correct option.

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